Periodontiis as a Complex Chaotic Dynamical Process

Methods: A time series analysis based on a differential equation describing periodontitis progression, formulates a model showing low amplitude chaos mixed with large amplitude relaxation canard orbits and a renormalization flow by a scaling law of 1.3. Local Lyapunov exponents suggest two zones of disease activity with a 3 times difference in disease rate between them. The fractal dimension of cementum is found 1.3 and is proposed as the power law of periodontal disease process. The model is tested with data from 162 periodontal patients, 43 of who were diagnosed as chronic cases (mean age 47±11), 68 as aggressive (mean age 26.2±7) and 51 as suspected for aggressive periodontitis (mean age 36±9.2) having severe disease but no family members with periodontitis. 36 periodontally healthy control subjects were recruited.

Results: Using a cut-off point at 1.2 times the mean value in healthy controls, as suggested by the model, the CD4/CD8 ratio discriminates chronic from aggressive cases with 71% sensitivity and 79% specificity. Similarly, CD20 with 64% and 81%, TNF-á with 70% and 71% and IL-4 with 62% and 70% sensitivity and specificity respectively. CD4/CD8 in parallel to CD20 yields 81% sensitivity and 75% specificity, and phagocytosis of polymorphonuclear cells 70% and 88% respectively. K-means cluster analysis on all data pooled, resulted in two homogenous groups of patients around mean values-centers of the clusters, corroborating the suggestion of two zones of disease activity made by the model.

Conclusion: The nonlinear model of this study identifies certain immunological parameters that can discriminate aggressive from chronic periodontitis cases, a feature useful to clinicians in decision making.